X3 Assignment X3.6 & past paper 201304 Q9

[Jun Wu]

Dear All

Hope you are well.

X3 Assignment X3.6

May I ask how per policy expense is calculated please?

We know - Per policy expenses are initially £1 per month throughout the life of the policy.

answer states:
1 Information on the per-policy expense is not very clear. Assume: £1 at 01/01/21, inflating at 1%
per month. For contracts starting 01/07/21, the starting amount is increased by 6 months of
inflation. So the present value of these expenses at inception is:
12 × 1.01^6 = 12.74 [1]

Q: are we saying we have 12 pound of total per policy expense as at 01/01/2021, but because average inception is 01/07/21, at which time the value would be inflated by 1.01^6?

2 The expenses are assumed to be paid after 9 months (3 months later than the expected average
date), so there is another 3 months to discount at 1%, giving £12.37

Q: (n) tells us expense is paid 9 months after inception, why is it 3 months later than the expected average date? what is this expected average date? and why do we have to discount it for 3 months?
I thought discounting is only for working out present value at 01/07/21?


If possible, do you know where I can find more similar questions like this one from past papers or chapter end summary?

past paper 201304 Q9

On the part on working out adjusted incurred
2008 - 600 = 764*0.55/0.7, where 0.7 is the ILF difference between limit 50 and 200.
etc

why do we *0.55 and where it is come from? and why do we /0.7 not *0.7? I always thought we * ILF to get the loss cost to layer.


Really appreciated for your help
Best regards
Jun

 

[Busy_Bee4422]

Hi Jun

1. For a policy starting 1/7 the per month expense will be 1*1.01^6. For the next month the per month expense will be 1*1.01^7 and it has to be discounted 1 month to get the PV on 1/7 giving you 1*1.01^6. The same applies for each of the next months till policy expires. Therefore, for the whole year on that date, the pv of expenses will be 12*1*1.01^6.

I got the impression this is one of the reasons they say the expense info isn't clear. Its unclear whether the expenses are fixed at what they are at policy inception thoughout the life of the policy or that's just the initial value. I have assumed its just the initial value.

2. The average payment date of the expenses is the middle of the policy i.e. after 6 months but they are being paid after nine months. This is three months of inflation so the amount is discounted.

3. There are different exesses and limits in each year so you first have to normalise the data i.e. adjust the past claims expereince so that it has the same excess and limit as in 2013.

The ILF for the layer of cover in 2008 is 0.7, 1.4 the factor at the 200 limit minus 0.7 the factor at the 50 excess limit. the 200 comes from 50 plus 150 which is the claim limit.
The ILF for the 2013 layer is 0.55 by the same reasoning. Therefore to normalise the 2008 data to change it to 2013 limits you divide by the ILF in 2008 and multiply by the ILF in 2013 i.e. 764*0.55/0.70.